Which string cores are the tightest

hex cores are generally tighter...although i haven't had much experience with tapered core strings, this means that the string tapers down to the core when it reaches the bridge, which generally provide a tighter, punchier sound...

 

Not really. When I did research for an article on bass strings for Guitar Player Magazine over 20 yrs ago, most manufacturers were moving or had moved to hex cores, not for their sound but primarily for quality control.

The hex cores give the first wrap something to "bite" into, so the string construction is less likely to lose its grip and come apart or loosen up, thereby throwing the string off-balance and ruining it. It also has the side effect of making the string stiffer. Other construction factors can make a string stiffer or more flexible.

The round core strings are less stiff, feel "floppier" only because of construction and resultant flexibility, but they aren't really tighter. And IMHO strings with round cores have more dimension and musicality. Thomastik Jazz Flats and Rounds, and DR Sunbeams are two examples of round core strings - I like them both very much.